Adjoint information

Look up adjoint in Wiktionary, the free dictionary. In mathematics, the term adjoint applies in several situations. Several of these share a similar formalism:...

{\displaystyle A} on an inner product space defines a Hermitian adjoint (or adjoint) operator A ∗ {\displaystyle A^{*}} on that space according to the...

this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics...

In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations...

names for the conjugate transpose of a matrix are Hermitian conjugate, adjoint matrix or transjugate. The conjugate transpose of a matrix A {\displaystyle...

In quantum field theory, the Dirac adjoint defines the dual operation of a Dirac spinor. The Dirac adjoint is motivated by the need to form well-behaved...

known as adjunct matrix, or "adjoint", though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is...

resulting in an isomorphism between the transpose and adjoint of u. The matrix of the adjoint of a map is the transposed matrix only if the bases are...

An adjoint equation is a linear differential equation, usually derived from its primal equation using integration by parts. Gradient values with respect...

The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It...

In mathematics, an adjoint bundle is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra...

self-adjoint operator is an operator equal to its own (formal) adjoint. If Ω is a domain in Rn, and P a differential operator on Ω, then the adjoint of...

Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces. The spectral...

the adjoint of T. It follows immediately from the above definition that the adjoint T ∗ {\displaystyle T^{*}} is closed. In particular, a self-adjoint operator...

transpose or algebraic adjoint of a linear map is often used to study the original linear map. This concept is generalised by adjoint functors. Let X # {\displaystyle...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

mathematics, the formal criteria for adjoint functors are criteria for the existence of a left or right adjoint of a given functor. One criterion is the...

This defines another bounded linear operator A* : H2 → H1, the adjoint of A. The adjoint satisfies A** = A. When the Riesz representation theorem is used...

In functional analysis, the Friedrichs extension is a canonical self-adjoint extension of a non-negative densely defined symmetric operator. It is named...

representable if and only if it has a left adjoint. The categorical notions of universal morphisms and adjoint functors can both be expressed using representable...

{\displaystyle (f\colon X\to Z)\mapsto (f^{Y}\colon X^{Y}\to Z^{Y})} , is a right adjoint to the product functor − × Y {\displaystyle -\times Y} . For this reason...

In signal processing, the adjoint filter mask h ∗ {\displaystyle h^{*}} of a filter mask h {\displaystyle h} is reversed in time and the elements are...

are then a pair of adjoint functors, with G {\displaystyle G} left-adjoint to F {\displaystyle F} and F {\displaystyle F} right-adjoint to G {\displaystyle...

and the θ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph. Hassler Whitney (1932) proved that with one...